Heavy Fermi Liquid Research Articles

Kondo breakdown in multi-orbital Anderson lattices induced by destructive hybridization interference

In this paper we consider a multi-band extension to the periodic Anderson model. We use a single site DMFT(NRG) in order to study the impact of the conduction band mediated effective hopping of the correlated electrons between the correlated orbitals onto the heavy Fermi-liquid formation. Whereas the hybridization of a single impurity model with two distinct conduction bands always adds up constructively, T_{K}\propto \exp(-\mathrm{const}\, U/(\Gamma_1+\Gamma_2))TK∝exp(−constU/(Γ1+Γ2)), we show that this does not have to be the case in lattice models, where, in remarkable contrast, also an low-energy Fermi-liquid scale T_0\propto \exp(-\mathrm{const}\, U/(\Gamma_1-\Gamma_2))T0∝exp(−constU/(Γ1−Γ2)) can emerge due to quantum interference effects in multi-band models, where UU denotes the local Coulomb matrix element of the correlated orbitals and \Gamma_iΓi the local hybridization strength of band ii. At high symmetry points, heavy Fermi-liquid formation is suppressed which is associated with a breakdown of the Kondo effect. This results in an asymptotically scale-invariant (i.e., power-law) spectrum of the correlated orbitals \propto|\omega|^{1/3}∝|ω|1/3, indicating non-Fermi liquid properties of the quantum critical point, and a small Fermi surface including only the light quasi-particles. This orbital selective Mott phase demonstrates the possibility of metallic local criticality within the general framework of ordinary single site DMFT.

Numerical signatures of ultra-local criticality in a one dimensional Kondo lattice model

Heavy fermion criticality has been a long-standing problem in condensed matter physics. Here we study a one-dimensional Kondo lattice model through numerical simulation and observe signatures of local criticality. We vary the Kondo coupling J_KJK at fixed doping x. At large positive J_KJK, we confirm the expected conventional Luttinger liquid phase with 2k_F=\frac{1+x}{2}2kF=1+x2 (in units of 2\pi2π), an analogue of the heavy Fermi liquid (HFL) in the higher dimension. In the J_K ≤ 0JK≤0 side, our simulation finds the existence of a fractional Luttinger liquid (LL\star⋆) phase with 2k_F=\frac{x}{2}2kF=x2, accompanied by a gapless spin mode originating from localized spin moments, which serves as an analogue of the fractional Fermi liquid (FL\star⋆) phase in higher dimensions. The LL\star⋆ phase becomes unstable and transitions to a spin-gapped Luther-Emery (LE) liquid phase at small positive J_KJK. Then we mainly focus on the “critical regime” between the LE phase and the LL phase. Approaching the critical point from the spin-gapped LE phase, we often find that the spin gap vanishes continuously, while the spin-spin correlation length in real space stays finite and small. For a certain range of doping, in a point (or narrow region) of J_KJK, the dynamical spin structure factor obtained through the time-evolving block decimation (TEBD) simulation shows dispersion-less spin fluctuations in a finite range of momentum space above a small energy scale (around 0.035 J0.035J) that is limited by the TEBD accuracy. All of these results are unexpected for a regular gapless phase (or critical point) described by conformal field theory (CFT). Instead, they are more consistent with exotic ultra-local criticality with an infinite dynamical exponent z=+z=+. The numerical discovery here may have important implications on our general theoretical understanding of the strange metals in heavy fermion systems. Lastly, we propose to simulate the model in a bilayer optical lattice with a potential difference.

Algebraic Hastatic Order in One-Dimensional Two-Channel Kondo Lattice.

The two-channel Kondo lattice likely hosts a rich array of phases, including hastatic order, a channel symmetry breaking heavy Fermi liquid. We revisit its one-dimensional phase diagram using density matrix renormalization group and, in contrast to previous work, find algebraic hastatic orders generically for stronger couplings. These are heavy Tomonaga-Luttinger liquids with nonanalyticities at Fermi vectors captured by hastatic density waves. We also find a predicted additional nonlocal order parameter due to interference between hastatic spinors, not present at large N, and residual repulsive interactions at strong coupling suggesting non-Fermi-liquid physics in higher dimensions.

Critical slowing down near a magnetic quantum phase transition with fermionic breakdown

When a system close to a continuous phase transition is subjected to perturbations, it takes an exceptionally long time to return to equilibrium. This critical slowing down is observed universally in the dynamics of bosonic excitations, such as order-parameter collective modes, but it is not generally expected to occur for fermionic excitations. Here using terahertz time-domain spectroscopy, we find evidence for fermionic critical slowing down in YbRh2Si2 close to a quantum phase transition between an antiferromagnetic phase and a heavy Fermi liquid. In the latter phase, the relevant quasiparticles are a quantum superposition of itinerant and localized electronic states with a strongly enhanced effective mass. As the temperature is lowered on the heavy-Fermi-liquid side of the transition, the heavy-fermion spectral weight builds up until the Kondo temperature TK ≈ 25 K, then decays towards the quantum phase transition and is, thereafter, followed by a logarithmic rise of the quasiparticle excitation rate below 10 K. A two-band heavy-Fermi-liquid theory shows that this is indicative of the fermionic critical slowing down associated with heavy-fermion breakdown near the quantum phase transition. The critical exponent of this breakdown could be used to classify this system among a wider family of fermionic quantum phase transitions that is yet to be fully explored.

Three-dimensional charge density wave in the dual heavy fermion system UPt2Si2

Heavy fermion liquids offer via their Kondo lattice diverse possibilities for exotic ground states. Using variable-temperature atomic pair distribution function analysis, we study the local atomic structure of the ``dual'' heavy fermion liquid $\mathrm{U}{\mathrm{Pt}}_{2}{\mathrm{Si}}_{2}$, which exhibits antiferromagnetism consistent with localized $5f$-electron states and transport properties characteristic to itinerant $5f$-``$spd$'' hybridized electron systems. We show that $\mathrm{U}{\mathrm{Pt}}_{2}{\mathrm{Si}}_{2}$ exhibits periodic lattice distortions (PLDs) involving both uranium and platinum atoms that are characteristic to three-dimensional charge density waves. The temperature evolution of the PLDs tracks that of the transport and magnetic properties, suggesting the presence of little-known $5f$-electron-lattice interactions. We argue that PLDs in heavy fermion liquids in general, and in particular in $\mathrm{U}{\mathrm{Pt}}_{2}{\mathrm{Si}}_{2}$, appear as new degrees of freedom that entangle competing electronic states and, as such, must be accounted for when their rich physics is considered.

Chiral Kondo lattice in doped MoTe2/WSe2 bilayers.

We theoretically study the interplay between magnetism and a heavy Fermi liquid in the AB-stacked transition metal dichalcogenide bilayer system, MoTe2/WSe2, in the regime in which the Mo layer supports localized magnetic moments coupled by interlayer electron tunneling to a weakly correlated band of itinerant electrons in the W layer. We show that the interlayer electron transfer leads to a chiral Kondo exchange, with consequences including a strong dependence of the Kondo temperature on carrier concentration and anomalous Hall effect due to a topological hybridization gap. The theoretical model exhibits two phases, a small Fermi surface magnet and a large Fermi surface heavy Fermi liquid; at the mean-field level, the transition between them is first order. Our results provide concrete experimental predictions for ongoing experiments on MoTe2/WSe2 bilayer heterostructures and introduces a controlled route to observe a topological selective Mott transition.

Spin chain on a metallic surface: Dissipation-induced order versus Kondo entanglement

We explore the physics of a spin-1/2 Heisenberg chain with Kondo interaction, $J_k$, to a two-dimensional electron gas. At weak $J_k$ the problem maps onto a Heisenberg chain locally coupled to a dissipative Ohmic bath. At the decoupled fixed point, the dissipation is a marginally relevant perturbation and drives long-range antiferromagnetic order along the chain. In the dynamical spin structure factor we observe a quadratic low-energy dispersion akin to Landau-damped Goldstone modes. At large $J_k$ Kondo screening dominates, and the spin correlations of the chain inherit the power law of the host metal, akin to a paramagnetic heavy Fermi liquid. In both phases we observe heavy bands near the Fermi energy in the composite-fermion spectral function. Our results, obtained from auxiliary-field quantum Monte Carlo simulations, provide a unique negative-sign-free realization of a quantum transition between an antiferromagnetic metal and a heavy-fermion metal. We discuss the relevance of our results in the context of scanning tunneling spectroscopy experiments of magnetic adatom chains on metallic surfaces.

Z2 metallic spin liquid on a frustrated Kondo lattice

Metallic spin liquid has been reported in several correlated metals, but a satisfactory theoretical description is not yet available. Here we propose a potential route to realize the metallic spin liquid and construct an effective $\mathbb{Z}_2$ gauge theory with charged fractionalized excitations on the triangular Kondo lattice. This leads to a $\mathbb{Z}_2$ metallic spin liquid featured with long-lived, heavy holon excitations of spin 0 and charge $+e$ and a partially enlarged electron Fermi surface. It differs from the weak-coupling FL$^*$ state proposed earlier and may be viewed as a fractionalized heavy fermion liquid. Our theory provides a general framework to describe the metallic spin liquid in frustrated Kondo lattice systems.

Solvable model for a charge- 4e superconductor

A charge-$4e$ superconductor forms due to the condensation of quartets of electrons. While in previous works the mechanism for the formation of charge-$4e$ superconductivity has been analyzed in terms of the binding of Cooper pairs in unconventional superconductors, its properties in the fermionic sector have not been studied systematically due to its inherently interacting nature even at the mean-field level. Here we propose a solvable model for a charge-$4e$ superconductor -- a spinful version of the Sachdev-Ye-Kitaev model with an anomalous quartic term. We show that the ground state is gapless and resembles a heavy Fermi liquid. We analytically solve for the superfluid density and show that it is perturbative in the strength of the charge-$4e$ order parameter, in sharp contrast with a regular (charge-$2e$) superconductor. Upon lowering temperature, we show that the correlation between charge-$4e$ order and regular interaction terms can drive a first-order phase transition to a charge-$2e$ superconducting state.

Gate-tunable heavy fermion quantum criticality in a moiré Kondo lattice

The authors propose a transition metal dichalcogenide moir\'e heterostructure that realizes a Kondo lattice and is capable of tuning across a quantum phase transition corresponding to the breakdown of Kondo screening. For a dual-gated setup, they theoretically identify the requisite gating conditions and find a quantum critical scenario where the local moments in a chiral spin-liquid state dissolve in the conduction electron Fermi sea to form an anomalous Hall heavy-fermion liquid. They discuss how the proposed gate-tunable Kondo lattice simulator can experimentally distinguish between various competing scenarios for the quantum phase transition, and thereby enable progress in the understanding of heavy-fermion quantum criticality.

Solvable theory of a strange metal at the breakdown of a heavy Fermi liquid

We introduce an effective theory for quantum critical points (QCPs) in heavy fermion systems, involving a change in carrier density without symmetry breaking. Our new theory captures a strongly coupled metallic QCP, leading to robust marginal Fermi liquid transport phenomenology, and associated linear in temperature ($T$) "strange metal" resistivity, all within a controlled large $N$ limit. In the parameter regime of strong damping of emergent bosonic excitations, the QCP also displays a near-universal "Planckian" transport lifetime, $\tau_{\mathrm{tr}}\sim\hbar/(k_BT)$. This is contrasted with the conventional so-called "slave boson" theory of the Kondo breakdown, where the large $N$ limit describes a weak coupling fixed point and non-trivial transport behavior may only be obtained through uncontrolled $1/N$ corrections. We also compute the weak-field Hall coefficient within the effective model as the system is tuned across the transition. We further find that between the two plateaus, reflecting the different carrier densities in the two Fermi liquid phases, the Hall coefficient can develop a peak in the critical crossover regime, like in recent experimental findings, in the parameter regime of weak boson damping.

Electronic spectra with paramagnon fractionalization in the single-band Hubbard model

We examine spectral properties of a recently proposed theory of the intermediate temperature pseudogap metal phase of the cuprates. We show that this theory can be obtained from the familiar paramagnon theory of nearly antiferromagnetic metals by fractionalizing the paramagnon into two ``hidden'' layers of $S=1/2$ spins. The first hidden layer of spins hybridizes with the electrons as in a Kondo lattice heavy Fermi liquid, whereas the second hidden layer of spins forms a spin liquid with fractionalized spinon excitations. We compute the imaginary part of the electronic self-energy induced by the spinon excitations. The energy and momentum dependence of the photoemission spectrum across the Brillouin zone provides a good match to observations by He et al. [Science 331, 1579 (2011)] in $({\mathrm{Pb}}_{x},{\mathrm{Bi}}_{2\ensuremath{-}x})({\mathrm{La}}_{y}{\mathrm{Sr}}_{2\ensuremath{-}y}){\mathrm{CuO}}_{6+\ensuremath{\delta}}$ and by Chen et al. [Science 366, 1099 (2019)] in ${(\mathrm{Bi},\mathrm{Pb})}_{2}{\mathrm{Sr}}_{2}\mathrm{Ca}{\mathrm{Cu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$.

Unconventional non-Fermi liquid properties of two-channel Anderson impurities system

A theory for treating the unconventional non-Fermi liquid temperature dependence of physical quantities, such as the resistivity, in the Pr-based two-channel Anderson impurities system is developed. It is shown that their temperature dependences are essentially the same as those in the pure lattice system except for the case of extremely low concentration of Pr ions that is difficult to realize by the controlled experiments. This result is consistent with recent observations in diluted Pr-1-2-20 system Y1−x Pr x Ir2Zn20 (x = 0.024, 0.044, 0.085, and 0.44) reported in Yamane et al (2018) Phys. Rev. Lett. 121, 077206, and is quite different from that in the case of single-channel Anderson impurities system in which the crossover between behaviors of the local Fermi liquid and heavy Fermi liquid occurs at around moderate concentration of impurities as observed in Ce-based heavy fermion system La1−x Ce x Cu6.

THz electrodynamics of mixed-valent YbAl$$_3$$ and LuAl$$_3$$ thin films

We present THz measurements of thin films of mixed-valent YbAl$_3$ and its structural analogue LuAl$_3$. Combined with traditional Fourier transform infrared (FTIR) spectroscopy, the extended Drude formalism is utilized to study the low-frequency transport of these materials. We find that LuAl$_3$ demonstrates conventional Drude transport whereas at low temperatures YbAl$_3$ demonstrates a sharply renormalized Drude peak and a mid-infrared (MIR) peak in the conductivity, indicative of the formation of a heavy Fermi liquid. In YbAl$_3$ the extended Drude framework shows a consistency of the scattering rate with Fermi-liquid behavior below $T < 40$ K and a moderate mass enhancement. While a $\omega^2$ Fermi liquid-like frequency dependence is not clearly exhibited, the temperature dependence of the Drude scattering rate and effective mass is consistent with the formation of a low-temperature moderately heavy Fermi liquid, albeit one with a smaller mass than observed in single crystals. The extended Drude analysis also supports a slow crossover between the Fermi liquid state and the normal state in YbAl$_3$.

Flat and correlated plasmon bands in graphene/α−RuCl3 heterostructures

We develop a microscopic theory for plasmon excitations of graphene/${\alpha}$-RuCl${_3}$ heterostructures. Within a Kondo-Kitaev model with various interactions, a heavy Fermi liquid hosting flat bands emerges in which the itinerant electrons of graphene effectively hybridize with the fractionalized fermions of the Kitaev quantum spin liquid. We find novel correlated plasmon bands induced by the interplay of flat bands and interactions and argue that our theory is consistent with the available experimental data on graphene/${\alpha}$-RuCl${_3}$ heterostructures. We predict novel plasmon branches beyond the long-wavelength limit and discuss the implications for probing correlation phenomena in other flat band systems.

Anomalous Quantum Oscillations in a Heterostructure of Graphene on a Proximate Quantum Spin Liquid.

The quasi-two-dimensional Mott insulator α-RuCl_{3} is proximate to the sought-after Kitaev quantum spin liquid (QSL). In a layer of α-RuCl_{3} on graphene, the dominant Kitaev exchange is further enhanced by strain. Recently, quantum oscillation (QO) measurements of such α-RuCl_{3} and graphene heterostructures showed an anomalous temperature dependence beyond the standard Lifshitz-Kosevich (LK) description. Here, we develop a theory of anomalous QO in an effective Kitaev-Kondo lattice model in which the itinerant electrons of the graphene layer interact with the correlated magnetic layer via spin interactions. At low temperatures, a heavy Fermi liquid emerges such that the neutral Majorana fermion excitations of the Kitaev QSL acquire charge by hybridizing with the graphene Dirac band. Using abinitio calculations to determine the parameters of our low-energy model, we provide a microscopic theory of anomalous QOs with a non-LK temperature dependence consistent with our measurements. We show how remnants of fractionalized spin excitations can give rise to characteristic signatures in QO experiments.

Competition of spinon Fermi surface and heavy Fermi liquid states from the periodic Anderson to the Hubbard model

We study a model of correlated electrons coupled by tunnelling to a layer of itinerant metallic electrons, which allows to interpolate from a frustrated limit favorable to spin liquid states to a Kondo-lattice limit favorable to interlayer coherent heavy metallic states. We study the competition of the spinon fermi surface state and the interlayer coherent heavy Kondo metal that appears with increasing tunnelling. Employing a slave rotor mean-field approach, we obtain a phase diagram and describe two regimes where the spin liquid state is destroyed by weak interlayer tunnelling, (i) the Kondo limit in which the correlated electrons can be viewed as localized spin moments and (ii) near the Mott metal-insulator-transition where the spinon Fermi surface transitions continuously into a Fermi liquid. We study the shape of LDOS spectra of the putative spin liquid layer in the heavy Fermi liquid phase and describe the temperature dependence of its width arising from quasiparticle interactions and disorder effects throughout this phase diagram, in an effort to understand recent STM experiments of the candidate spin liquid 1T-TaSe$_2$ residing on metallic 1H-TaSe$_2$. Comparison of the shape and temperature dependence of the theoretical and experimental LDOS suggest that this system is either close to the localized Kondo limit, or in an intermediate coupling regime where the Kondo coupling and the Heisenberg exchange interaction are comparable.

Kondo Breakdown in a Spin-1/2 Chain of Adatoms on a Dirac Semimetal.

We consider a spin-1/2 Heisenberg chain coupled via a Kondo interaction to two-dimensional Dirac fermions. The Kondo interaction is irrelevant at the decoupled fixed point, leading to the existence of a Kondo-breakdown phase and a Kondo-breakdown critical point separating such a phase from a heavy Fermi liquid. We reach this conclusion on the basis of a renormalization group analysis, large-N calculations as well as extensive auxiliary-field quantum MonteCarlo simulations. We extract quantities such as the zero-bias tunneling conductance which will be relevant to future experiments involving adatoms on semimetals such as graphene.

Periodically Driven Sachdev-Ye-Kitaev Models.

Periodically driven quantum matter can realize exotic dynamical phases. In order to understand how ubiquitous and robust these phases are, it is pertinent to investigate the heating dynamics of generic interacting quantum systems. Here we study the thermalization in a periodically driven generalized Sachdev-Ye-Kitaev (SYK) model, which realizes a crossover from a heavy Fermi liquid (FL) to a non-Fermi liquid (NFL) at a tunable energy scale. Developing an exact field theoretic approach, we determine two distinct regimes in the heating dynamics. While the NFL heats exponentially and thermalizes rapidly, we report that the presence of quasiparticles in the heavy FL obstructs heating and thermalization over comparatively long timescales. Prethermal high-frequency dynamics and possible experimental realizations of nonequilibrium SYK physics are discussed as well.

Intrinsic superconducting instabilities of a solvable model for an incoherent metal

We construct a family of translationally invariant lattice models with a large number ($N$) of orbitals at every site coupled together via single electron tunneling. By tuning the relative strength of the electronic bandwidth and on-site interactions, that have a modified Sachdev-Ye-Kitaev (SYK) form, we demonstrate a number of unusual features at strong coupling and in the large$-N$ limit. We find examples of (i) an intrinsic non-BCS superconducting instability arising out of an incoherent non-Fermi liquid metal, and, (ii) an instability of an incipient heavy Fermi liquid metal to superconductivity with transition temperatures comparable to its renormalized bandwidth. At strong-coupling, these solvable models display pairing instabilities that are not driven by any special "nesting" properties associated with an underlying Fermi surface.